let`s start

2026-06-27 17:36:46 +03:00 · 2026-06-27 17:36:46 +03:00 · 2e7f992c86
commit 2e7f992c86
59 changed files with 108491 additions and 0 deletions
--- a/1
+++ b/1
@ -0,0 +1 @@
 latexmk -pdf -outdir=pdf -auxdir=tmp templates/model_analitic.tex && latexmk -c -outdir=pdf -auxdir=tmp templates/model_analitic.tex
--- a/data/processed/MEM_16M_B.csv
+++ b/data/processed/MEM_16M_B.csv
@ -0,0 +1,345 @@
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--- a/data/processed/MEM_16M_R.csv
+++ b/data/processed/MEM_16M_R.csv
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--- a/data/processed/MEM_1M_B.csv
+++ b/data/processed/MEM_1M_B.csv
@ -0,0 +1,637 @@
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--- a/data/processed/MEM_1M_R.csv
+++ b/data/processed/MEM_1M_R.csv
@ -0,0 +1,535 @@
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--- a/data/processed/MEM_4M_B.csv
+++ b/data/processed/MEM_4M_B.csv
@ -0,0 +1,396 @@
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--- a/data/processed/MEM_4M_R.csv
+++ b/data/processed/MEM_4M_R.csv
@ -0,0 +1,471 @@
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--- a/data/processed/MRZ_2.178_16.7M_B.csv
+++ b/data/processed/MRZ_2.178_16.7M_B.csv
--- a/data/processed/MRZ_2.178_16.7M_R.csv
+++ b/data/processed/MRZ_2.178_16.7M_R.csv
--- a/data/processed/MRZ_2.178_5.6M_B.csv
+++ b/data/processed/MRZ_2.178_5.6M_B.csv
--- a/data/processed/MRZ_2.178_5.6M_R.csv
+++ b/data/processed/MRZ_2.178_5.6M_R.csv
--- a/data/processed/MRZ_2.178_50M_B.csv
+++ b/data/processed/MRZ_2.178_50M_B.csv
--- a/data/processed/MRZ_2.178_50M_R.csv
+++ b/data/processed/MRZ_2.178_50M_R.csv
--- a/data/raw/0_MEM_p2f3.xlsx
+++ b/data/raw/0_MEM_p2f3.xlsx
--- a/data/raw/0_MRZ_2_178_p1f3.csv
+++ b/data/raw/0_MRZ_2_178_p1f3.csv
--- a/data/raw/MEM_16M_B.csv
+++ b/data/raw/MEM_16M_B.csv
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--- a/data/raw/MEM_16M_R.csv
+++ b/data/raw/MEM_16M_R.csv
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--- a/data/raw/MEM_1M_B.csv
+++ b/data/raw/MEM_1M_B.csv
@ -0,0 +1,637 @@
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--- a/data/raw/MEM_1M_R.csv
+++ b/data/raw/MEM_1M_R.csv
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--- a/data/raw/MEM_4M_B.csv
+++ b/data/raw/MEM_4M_B.csv
@ -0,0 +1,396 @@
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--- a/data/raw/MEM_4M_R.csv
+++ b/data/raw/MEM_4M_R.csv
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--- a/data/raw/MRZ_2.178_16.7M_B.csv
+++ b/data/raw/MRZ_2.178_16.7M_B.csv
--- a/data/raw/MRZ_2.178_16.7M_R.csv
+++ b/data/raw/MRZ_2.178_16.7M_R.csv
--- a/data/raw/MRZ_2.178_5.6M_B.csv
+++ b/data/raw/MRZ_2.178_5.6M_B.csv
--- a/data/raw/MRZ_2.178_5.6M_R.csv
+++ b/data/raw/MRZ_2.178_5.6M_R.csv
--- a/data/raw/MRZ_2.178_50M_B.csv
+++ b/data/raw/MRZ_2.178_50M_B.csv
--- a/data/raw/MRZ_2.178_50M_R.csv
+++ b/data/raw/MRZ_2.178_50M_R.csv
--- a/data/raw/TEA_TPA_TBA_TPentA_p4f2.csv
+++ b/data/raw/TEA_TPA_TBA_TPentA_p4f2.csv
@ -0,0 +1,532 @@
 TEA_0.63mM,,TEA_1.25mM,,TEA_2.5mM,,TEA_5mM,,TPA_0.31mM,,TPA_0.63mM3,,TPA_1.25mM,,TPA_2.5mM,,TPA_5mM,,TBA_0.25mM,,TBA_0.5mM,,Dataset 11,,Dataset 12,,Dataset 13,,Dataset 14,,Dataset 15,,Dataset 16,,Dataset 17,,Dataset 18,,Dataset 19,
 X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y,X,Y
 -19.749328148241872,17.3287114169296,-19.854740327590708,13.869264041922074,,,-19.925015113823267,6.911687064440956,-14.267894822102335,17.250787251310655,-14.239784907609312,13.806203304541695,-14.40844439456745,10.406147452412126,-14.471691702176754,6.868775911785665,-14.506829095293032,3.4996285275831607,-8.814571410455821,17.194505232248282,-8.870791239441868,13.761364259520732,,,,,,,,,,,,,,,,,,
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--- a/img/MEM_p2f3.jpg
+++ b/img/MEM_p2f3.jpg
--- a/img/MRZ_2_178_p1f2.gif
+++ b/img/MRZ_2_178_p1f2.gif
--- a/img/TBA_p3f3.gif
+++ b/img/TBA_p3f3.gif
--- a/img/TEA_TPA_TBA_TPentA_p4f2.jpg
+++ b/img/TEA_TPA_TBA_TPentA_p4f2.jpg
--- a/models/1.tex
+++ b/models/1.tex
@ -0,0 +1,208 @@
 \documentclass[12pt,a4paper]{article}
 % Настройки для работы с русским языком в XeLaTeX
 \usepackage{fontspec} 
 \usepackage{polyglossia} 
 \setmainlanguage{russian}
 \setotherlanguage{english}
 % Базовые шрифты (используют стандартные системные шрифты)
 \setmainfont{Times New Roman} 
 \newfontfamily{\cyrillicfont}{Times New Roman}
 % Математика и графика
 \usepackage{amsmath, amssymb, amsfonts}
 \usepackage{graphicx}
 % Геометрия страницы
 \usepackage{geometry}
 \geometry{top=2cm, bottom=2cm, left=2.5cm, right=2cm}
 % Списки и ссылки
 \usepackage{enumitem}
 \usepackage{hyperref}
 % Схемы моделей
 \usepackage{tikz}
 \usetikzlibrary{arrows.meta}
 \title{Кинетическая модель \textbf{№5} \\ NMDA-канала}
 \author{Теоретический вывод}
 \date{}
 \begin{document}
 \maketitle
 \section{Схема модели}
 \begin{center}
 \begin{figure}[h!]
 \centering
 \begin{tikzpicture}[->, >=Stealth, node distance=2cm, thick]
    % Узлы (вещества)
    \node (O*) {$O^*$};
    \node (O_B) [right of=O*] {$O_B$};
    % Переходы (реакции)
    % Верхняя стрелка смещена на 2pt вверх, нижняя — на 2pt вниз
    \draw ([yshift=2pt]O*.east) -- ([yshift=2pt]O_B.west) node [midway, above] {$k_1[B]$};
    \draw ([yshift=-2pt]O_B.west) -- ([yshift=-2pt]O*.east) node [midway, below] {$k_2$};
 \end{tikzpicture}
 \end{figure}
 \end{center}
 \textbf{Обозначения:}
 \begin{itemize}
    \item $O^*$ – открытый (проводящий) канал, связанный с агонистом
    \item $O_B$ – открытый заблокированный канал
    \item $[B]$ – концентрация блокатора (переменная)
    \item $k_1, k_2$ – константы связывания/диссоциации блокатора
 \end{itemize}
 \section{Дифференциальные уравнения}
 Система обыкновенных дифференциальных уравнений, описывающая изменение вероятности обнаружения канала в каждом состоянии, имеет вид:
 \[
 \begin{cases}
 \dfrac{d[O^*]}{dt} = -k_1[B][O^*] + k_2[O_B] \\\\
 \dfrac{d[O_B]}{dt} = k_1[B][O^*] - k_2[O_B]
 \end{cases}
 \]
 Условие нормировки:
 \[
 [O^*] + [O_B] = 1
 \]
 \section{Решение системы дифференциальных уравнений}
 \subsection{Матричная форма}
 Система может быть записана как:
 \[
 \frac{d\mathbf{X}}{dt} = \mathbf{A} \mathbf{X},
 \]
 где 
 \[
 \mathbf{X} = \begin{pmatrix}
 [O^*] \\ [O_B]
 \end{pmatrix}; \; 
 \mathbf{A} = \begin{pmatrix}
 -k_1[B] & k_2 \\
 k_1[B] & -k_2 \\
 \end{pmatrix}
 \]
 \subsection{Нахождение собственных значений}
 Решение ищется в виде 
 \[
 \mathbf{X}(t) = e^{At}C
 \]
 Собственные числа матрицы определяются как корни её характерестическим многочленом 
 \[
 \chi_A(\lambda)= |A-\lambda I| = k_1[B] \lambda + k_2 \lambda + \lambda^2 = 0
 \]
 \[\begin{cases}
    \lambda_1 = 0 \\
    \lambda_2 = -k_1[B] - k_2
 \end{cases}\]
 Собственные вектора определяются как базис решения 
 \[A - \lambda_i I = 0\]
 \[
    v_1 = \begin{pmatrix}\frac{k_2}{k_1[B]}\\1\end{pmatrix};\;
    v_2 = \begin{pmatrix}-1\\1\end{pmatrix}
 \]
 Тогда можно диаганализовать $A = (v_1, v_2) \cdot diag(\lambda_1, \lambda_2) (v_1, v_2)^{-1}$ и получить
 \[
 X(t) = P\exp(diag(\lambda_1, \lambda_2)t)C
 \]
 Имеем
 \[
 \begin{pmatrix}
    [O^*] \\ [O_B]
 \end{pmatrix} = 
 \begin{pmatrix}
    \frac{k_2}{k_1[B]} & -1 \\
    1 & 1
 \end{pmatrix}
 \begin{pmatrix}
    1 & 0 \\
    0 & e^{(-k_1[B] - k_2)t}
 \end{pmatrix}
 \begin{pmatrix}
    C_1 \\ C_2
 \end{pmatrix}
 \]
 Или
 \[\begin{cases}
    [O^*] = \frac{k_{2}}{k_{1}[B]}C_{1}-C_{2}e^{-(k_{1}[B]+k_{2})t} \\
    [O_B] = C_{1}+C_{2}e^{-(k_{1}[B]+k_{2})t}
 \end{cases}\]
 Константы определяются через начальное состояние
 \[\begin{cases}
    [O^*](0) = \frac{k_{2}}{k_{1}[B]}C_{1}-C_{2} \\
    [O_B](0) = C_{1}+C_{2} \\
    [O^*](0) + [O_B](0) = 1
 \end{cases}
 ;\;
 \begin{cases}
    C_1 = \frac{k_{1}[B]}{k_{1}[B] + k_{2}} \\
    C_2 = \frac{k_2}{k_{1}[B] + k_{2}} - [O^*](0)
 \end{cases}\]
 Тогда имеем
 \[[O^*](t) = \frac{k_2}{k_{1}[B] + k_{2}} + ([O^*](0) - \frac{k_2}{k_{1}[B] + k_{2}})e^{-(k_{1}[B]+k_{2})t}\]
 \subsection{Ток через мембрану}
 Величина тока пропорциональна концентрации открытых каналов
 \[I(t) = I_{S} \cdot [O^*](t)\]
 Где $I_{S}$ - это стационарный ток, максимального открытия каналов
 \[\frac{I(t)}{I_{S}} = \frac{k_2}{k_{1}[B] + k_{2}} + ([O^*](0) - \frac{k_2}{k_{1}[B] + k_{2}})e^{-(k_{1}[B]+k_{2})t}\]
 В процессе блокады, $[O^*](0) = 1$
 \[\frac{I(t)_{on}}{I_{S}} = \frac{k_2}{k_{1}[B] + k_{2}} + \frac{k_1[B]}{k_{1}[B] + k_{2}}e^{-(k_{1}[B]+k_{2})t}\]
 Введём обозначения
 \[\begin{cases}
    A = \frac{k_{1}[B]}{k_{1}[B] + k_{2}} \\
    \tau_{on} = \frac{1}{k_{1}[B]+k_{2}} \\
    \tau_{off} = \frac{1}{k_2}
 \end{cases}
 \]
 \[\frac{{I(t)}_{on}}{I_{S}} = (1-A) + Ae^{-t/\tau}\]
 В процессе релаксации 
 \[
 \begin{cases}
    [O^*](0) = \lim_{t \to +\infty} \frac{{I(t)}_{on}}{I_{S}} = 1 - A \\
    [B] = 0
 \end{cases}
 \]
 \[\frac{I(t)_{off}}{I_{S}} = 1 - Ae^{-t/\tau_off}\]
 \section{Вычисление констант из экспериментальных данных}
 \[\begin{cases}
    k_2 = \frac{1}{\tau_{s}}\\
    k_1 = \dfrac{\tau_{off} - \tau_{on}}{[B]\tau_{on}\tau_{off}}
 \end{cases}\]
 \end{document}
--- a/models/models_list.tex
+++ b/models/models_list.tex
@ -0,0 +1,123 @@
 \documentclass[12pt,a4paper]{article}
 \usepackage{fontspec}
 \usepackage{polyglossia}
 \setmainlanguage{russian}
 \setotherlanguage{english}
 \setmainfont{Times New Roman}
 \newfontfamily{\cyrillicfont}{Times New Roman}
 \usepackage{amsmath, amssymb}
 \usepackage{geometry}
 \geometry{top=2cm, bottom=2cm, left=2cm, right=2cm}
 \usepackage{tikz}
 \usetikzlibrary{arrows.meta, positioning}
 \begin{document}
 \section*{Полные кинетические схемы}
 \subsection*{Модель 1: Односайтовый блок открытого канала}
 \begin{center}
 \begin{tikzpicture}[->, >=Stealth, node distance=1.5cm, thick]
    \node (O) {$O$};
    \node (OB) [right=of O] {$OB$};
    \draw ([yshift=2pt]O.east) -- ([yshift=2pt]OB.west) node[midway, above] {$k_1[B]$};
    \draw ([yshift=-2pt]OB.west) -- ([yshift=-2pt]O.east) node[midway, below] {$k_2$};
 \end{tikzpicture}
 \end{center}
 \vspace{1cm}
 \subsection*{Модель 2: Двухсайтовая последовательная блокада открытого канала}
 \begin{center}
 \begin{tikzpicture}[->, >=Stealth, node distance=1.5cm, thick]
    \node (O) {$O$};
    \node (B1) [right=of O] {$OB_1$};
    \node (B2) [right=of B1] {$OB_2$};
    \draw ([yshift=2pt]O.east) -- ([yshift=2pt]B1.west) node[midway, above] {$k_1[B]$};
    \draw ([yshift=-2pt]B1.west) -- ([yshift=-2pt]O.east) node[midway, below] {$k_2$};
    \draw ([yshift=2pt]B1.east) -- ([yshift=2pt]B2.west) node[midway, above] {$k_3[B]$};
    \draw ([yshift=-2pt]B2.west) -- ([yshift=-2pt]B1.east) node[midway, below] {$k_4$};
 \end{tikzpicture}
 \end{center}
 \vspace{1cm}
 \subsection*{Модель 3: Ловушечный блок (trapping) -- полная схема}
 \begin{center}
 \begin{tikzpicture}[->, >=Stealth, node distance=2.5cm, thick]
    % Состояния
    \node (O) {$O$};
    \node (B1) [right=of O] {$OB_1$};
    \node (B2) [right=of B1] {$OB_2$};
    \node (C) [below=of O, yshift=-1cm] {$C$};
    \node (CB) [below=of B2, yshift=-1cm] {$C_{B}$};
    % Горизонтальные переходы (блок/деблок)
    \draw (O) -- (B1) node[midway, above] {$k_1[\text{B}]$};
    \draw (B1) -- (O) node[midway, below] {$k_{-1}$};
    \draw (B1) -- (B2) node[midway, above] {$k_2$};
    \draw (B2) -- (B1) node[midway, below] {$k_{-2}$};
    % Вертикальные переходы (ворота)
    \draw (O) -- (C) node[midway, left] {$\alpha$};
    \draw (C) -- (O) node[midway, right] {$\beta$};
    \draw (B2) -- (CB) node[midway, left] {$\gamma$};
    \draw [->, dashed] (CB) -- (B2) node[midway, right] {$\delta$ (оч. медл.)};
    % Отметка, что OB1 не переходит в CB
    % \node[draw=red, dashed, inner sep=0pt, fit=(B1) (CB), label={[red]right:нет перехода}] {};
 \end{tikzpicture}
 \end{center}
 \vspace{1cm}
 \subsection*{Модель 4: Преблокада закрытого канала -- полная схема}
 \begin{center}
 \begin{tikzpicture}[->, >=Stealth, node distance=2.5cm, thick]
    % Состояния
    \node (C) {$C$};
    \node (CB) [right=of C] {$C_{B}$};
    \node (OB2) [below=of CB, yshift=-1cm] {$OB_2$};
    \node (O) [left=of OB2, yshift=0cm] {$O$};
    \node (OB1) [above=of O, yshift=0.5cm] {$OB_1$};
    % Переходы в закрытом состоянии
    \draw (C) -- (CB) node[midway, above] {$k_{\text{pre}}[\text{B}]$};
    \draw (CB) -- (C) node[midway, below] {$k_{\text{off,pre}}$};
    % Активация из закрытого блокированного в открытый блокированный (глубокий сайт)
    \draw (CB) -- (OB2) node[midway, right] {$\alpha'$};
    % Связывание глубокого сайта из открытого состояния (для полноты)
    \draw (O) -- (OB1) node[midway, above] {$k_1[\text{B}]$};
    \draw (OB1) -- (O) node[midway, below] {$k_{-1}$};
    \draw (OB1) -- (OB2) node[midway, right] {$k_2$};
    \draw (OB2) -- (OB1) node[midway, left] {$k_{-2}$};
    % Диссоциация из OB2 в открытое O (минуя OB1?) – для простоты можно изобразить возврат через OB1
    % Активация незаблокированного канала
    \draw (C) -- (O) node[midway, left] {$\alpha$};
 \end{tikzpicture}
 \end{center}
 \vspace{1cm}
 \subsection*{Модель 5: Размерно-селективный trapping -- полная схема}
 \begin{center}
 \begin{tikzpicture}[->, >=Stealth, node distance=2.5cm, thick]
    % Состояния
    \node (O) {$O$};
    \node (OB1) [right=of O] {$OB_1$};
    \node (OB2) [right=of OB1] {$OB_2$};
    \node (C) [below=of O, yshift=-1cm] {$C$};
    \node (CB) [below=of OB2, yshift=-1cm] {$C_{B}$};
    \node (esc) [below=of CB, yshift=-0.8cm, text width=2cm, align=center] {Выход в\\ цитоплазму};
    % Горизонтальные связывания
    \draw (O) -- (OB1) node[midway, above] {$k_1[\text{B}]$};
    \draw (OB1) -- (O) node[midway, below] {$k_{-1}$};
    \draw (OB1) -- (OB2) node[midway, above] {$k_2$};
    \draw (OB2) -- (OB1) node[midway, below] {$k_{-2}$};
    % Воротные переходы
    \draw (O) -- (C) node[midway, left] {$\alpha,\beta$};
    \draw (OB2) -- (CB) node[midway, right] {$\gamma$};
    \draw [->, dashed] (CB) -- (OB2) node[midway, left] {$\delta$ (медл.)};
    % Размерно-селективный выход
    \draw [->, red, thick] (CB) -- (esc) node[midway, right] {\small $k_{\text{esc}}(r)$};
    \node [red] at (6,-4) {$r$ -- радиус иона};
 \end{tikzpicture}
 \end{center}
 \end{document}
--- a/models/pdf/1.pdf
+++ b/models/pdf/1.pdf
--- a/models/pdf/1.synctex.gz
+++ b/models/pdf/1.synctex.gz
--- a/models/pdf/models_list.pdf
+++ b/models/pdf/models_list.pdf
--- a/models/pdf/models_list.synctex.gz
+++ b/models/pdf/models_list.synctex.gz
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+++ b/models/tmp/1.aux
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--- a/models/tmp/models_list.xdv
+++ b/models/tmp/models_list.xdv
--- a/1998.pdf
+++ b/1998.pdf
--- a/1998.pdf
+++ b/1998.pdf
--- a/1999.pdf
+++ b/1999.pdf
--- a/1999.pdf
+++ b/1999.pdf
--- a/receptors...
+++ b/receptors...
--- a/papers/merge.pdf
+++ b/papers/merge.pdf
--- a/scripts/main.py
+++ b/scripts/main.py
@ -0,0 +1,47 @@
 import matplotlib.pyplot as plt
 import pandas as pd
 import numpy as np
 def plot_csv(file_path):
    df = pd.read_csv(file_path, decimal=',', sep=';')
    plt.plot(df.iloc[1:, 0], df.iloc[1:, 1], linewidth=0.5)
    plt.title(file_path)
    plt.xlabel(df.columns[0])
    plt.ylabel(df.columns[1])
    plt.grid(True)
    plt.show()
 def shift_x_to_zero(input_file, output_file):
    df = pd.read_csv(input_file, decimal=',', sep=';')
    df.iloc[1:, 0] = df.iloc[1:, 0] - df.iloc[1:, 0].iloc[0]
    df.to_csv(output_file, index=False, decimal=',', sep=';')
 def normalize_current(input_path, output_path, frac_avg=0.05):
    df = pd.read_csv(input_path, sep=';', decimal=',')
    t = df.iloc[:, 0].values
    I = df.iloc[:, 1].values
    n = len(I)
    n_avg = max(1, int(n * frac_avg))
    first_mean = np.mean(I[:n_avg])
    last_mean = np.mean(I[-n_avg:])
    if first_mean > last_mean:
        I_max = first_mean
        I_min = last_mean
    else:
        I_max = last_mean
        I_min = first_mean
    I_norm = 1-(I - I_min)/abs(I_max - I_min)
    out = pd.DataFrame({'Time': t, 'I_norm': I_norm})
    out.to_csv(output_path, sep=';', decimal=',', index=False)
 files = ["MEM_16M_B.csv", "MEM_1M_B.csv", "MEM_4M_B.csv", "MRZ_2.178_16.7M_B.csv", "MRZ_2.178_5.6M_B.csv", "MRZ_2.178_50M_B.csv", "MEM_16M_R.csv", "MEM_1M_R.csv", "MEM_4M_R.csv", "MRZ_2.178_16.7M_R.csv", "MRZ_2.178_5.6M_R.csv", "MRZ_2.178_50M_R.csv"]
 dir1 = "data/raw/"
 dir2 = "data/processed/"
 for file in files:
    shift_x_to_zero(dir1 + file, dir2 + file)
    normalize_current(dir2 + file, dir2 + file)
    plot_csv(dir2 + file)
    # plot_csv(dir1 + file)
--- a/templates/model_analitic.tex
+++ b/templates/model_analitic.tex
@ -0,0 +1,209 @@
 \documentclass[12pt,a4paper]{article}
 \usepackage[T2A]{fontenc}
 \usepackage[utf8]{inputenc}
 \usepackage[russian]{babel}
 \usepackage{amsmath, amssymb, amsfonts}
 \usepackage{graphicx}
 \usepackage{geometry}
 \geometry{top=2cm, bottom=2cm, left=2.5cm, right=2cm}
 \usepackage{enumitem}
 \usepackage{hyperref}
 \title{Кинетическая модель \textbf{<Название модели>} \\ NMDA-канала}
 \author{Теоретический вывод}
 \date{}
 \begin{document}
 \maketitle
 \section{Схема модели}
 \begin{center}
 % Здесь будет графическая или текстовая схема переходов
 % Пример:
 % \[
 % C \xrightleftharpoons[l_2]{l_1[A]} C_A \xrightleftharpoons[\alpha]{\beta} O^* \xrightleftharpoons[k_2]{k_1[B]} O_B
 % \]
 \end{center}
 \textbf{Обозначения:}
 \begin{itemize}[label=--]
    \item $C$ – закрытый канал, не связанный с агонистом
    \item $C_A$ – закрытый канал, связанный с агонистом
    \item $O^*$ – открытый (проводящий) канал, связанный с агонистом
    \item $O_B$ – открытый заблокированный канал
    \item $[A]$ – концентрация агониста (постоянная)
    \item $[B]$ – концентрация блокатора (переменная)
    \item $l_1, l_2$ – константы связывания/диссоциации агониста
    \item $\beta, \alpha$ – константы открытия/закрытия канала
    \item $k_1, k_2$ – константы связывания/диссоциации блокатора
 \end{itemize}
 \section{Дифференциальные уравнения}
 Система обыкновенных дифференциальных уравнений, описывающая изменение вероятностей нахождения канала в каждом состоянии, имеет вид:
 \[
 \begin{cases}
 \dfrac{d[C]}{dt} = -l_1[A][C] + l_2[C_A] \\[10pt]
 \dfrac{d[C_A]}{dt} = l_1[A][C] - (l_2 + \beta)[C_A] + \alpha[O^*] \\[10pt]
 \dfrac{d[O^*]}{dt} = \beta[C_A] - (\alpha + k_1[B])[O^*] + k_2[O_B] \\[10pt]
 \dfrac{d[O_B]}{dt} = k_1[B][O^*] - k_2[O_B]
 \end{cases}
 \]
 Условие нормировки:
 \[
 [C] + [C_A] + [O^*] + [O_B] = 1.
 \]
 \section{Решение системы дифференциальных уравнений}
 \subsection{Матричная форма}
 Система может быть записана как:
 \[
 \frac{d\mathbf{X}}{dt} = \mathbf{A} \mathbf{X},
 \]
 где $\mathbf{X} = ([C], [C_A], [O^*], [O_B])^T$, а $\mathbf{A}$ – матрица коэффициентов.
 Для данной модели матрица $\mathbf{A}$ имеет вид:
 \[
 \mathbf{A} = \begin{pmatrix}
 -l_1[A] & l_2 & 0 & 0 \\
 l_1[A] & -(l_2+\beta) & \alpha & 0 \\
 0 & \beta & -(\alpha+k_1[B]) & k_2 \\
 0 & 0 & k_1[B] & -k_2
 \end{pmatrix}.
 \]
 \subsection{Нахождение собственных значений}
 Решение ищется в виде $\mathbf{X}(t) = \sum_{i=1}^{4} C_i \mathbf{v}_i e^{\lambda_i t}$, где $\lambda_i$ – собственные значения $\mathbf{A}$ (корни характеристического полинома $|\mathbf{A} - \lambda\mathbf{I}| = 0$).
 Одно из собственных значений всегда равно нулю ($\lambda_1 = 0$), остальные $\lambda_2, \lambda_3, \lambda_4$ – отрицательные действительные числа (или комплексно-сопряжённые с отрицательной действительной частью).
 Для быстрых блокаторов ($k_2$ велика) и при насыщающей концентрации агониста система упрощается: переходы $C \to C_A \to O^*$ считаются быстрыми, и модель редуцируется до двух экспонент.
 \subsection{Двухэкспоненциальная аппроксимация}
 В условиях непрерывного присутствия агониста (высокая $[A]$) и когда блокировка медленнее активации, кинетика тока $I(t)$ при добавлении или удалении блокатора описывается суммой двух экспонент:
 \[
 I(t) = I_S + (I_B - I_S) \left[ A_{fast} e^{-t/\tau_{fast}} + (1 - A_{fast}) e^{-t/\tau_{slow}} \right],
 \]
 где:
 \begin{itemize}
    \item $I_S$ – стационарный ток до применения блокатора,
    \item $I_B$ – стационарный ток в присутствии блокатора,
    \item $A_{fast}$ – амплитуда быстрой компоненты,
    \item $\tau_{fast}, \tau_{slow}$ – быстрая и медленная постоянные времени.
 \end{itemize}
 \subsection{Связь $\tau_{fast}, \tau_{slow}$ с кинетическими константами}
 Для модели <название модели> получены следующие соотношения (приводятся в соответствующем разделе литературы):
 \[
 \frac{1}{\tau_{fast}} = \lambda_2 = \frac{1}{2}\left( P + Q - \sqrt{(P-Q)^2 + 4R} \right),
 \]
 \[
 \frac{1}{\tau_{slow}} = \lambda_3 = \frac{1}{2}\left( P + Q + \sqrt{(P-Q)^2 + 4R} \right),
 \]
 где $P, Q, R$ – функции констант $k_1, k_2, k_3, k_4$ и концентраций $[A], [B]$.
 В частном случае (для модели последовательного связывания двух молекул) получаем:
 \[
 \frac{1}{\tau_{fast}^{off}} = k_2, \quad \frac{1}{\tau_{slow}^{off}} = k_4,
 \]
 \[
 \frac{1}{\tau_{fast}^{on}} = k_1[B] + k_2, \quad \frac{1}{\tau_{slow}^{on}} = k_3[B] + k_4.
 \]
 \section{Вычисление констант из экспериментальных данных}
 \subsection{Необходимые экспериментальные данные}
 Для определения неизвестных кинетических параметров модели требуются следующие измерения (при фиксированной концентрации агониста $[A] = const$, обычно насыщающей):
 \begin{enumerate}
    \item Зависимость $\tau_{fast}^{on}$ и $\tau_{slow}^{on}$ от концентрации блокатора $[B]$.
    \item Зависимость $\tau_{fast}^{off}$ и $\tau_{slow}^{off}$ от $[B]$ (обычно постоянны).
    \item Амплитуда быстрой компоненты $A_{fast}^{off}$ как функция $[B]$.
    \item Стационарная блокада $I_B/I_S$ как функция $[B]$.
 \end{enumerate}
 \subsection{Алгоритм расчёта констант}
 \subsubsection{Шаг 1. Определение $k_2$ и $k_4$}
 Если модель предсказывает независимость $\tau_{fast}^{off}$ и $\tau_{slow}^{off}$ от $[B]$, то:
 \[
 k_2 = \frac{1}{\tau_{fast}^{off}}, \quad k_4 = \frac{1}{\tau_{slow}^{off}}.
 \]
 \subsubsection{Шаг 2. Определение $k_1$ и $k_3$}
 Из зависимостей $\tau_{fast}^{on}([B])$ и $\tau_{slow}^{on}([B])$:
 \[
 \frac{1}{\tau_{fast}^{on}} = k_1 [B] + k_2 \quad \Rightarrow \quad k_1 = \frac{d(1/\tau_{fast}^{on})}{d[B]},
 \]
 \[
 \frac{1}{\tau_{slow}^{on}} = k_3 [B] + k_4 \quad \Rightarrow \quad k_3 = \frac{d(1/\tau_{slow}^{on})}{d[B]}.
 \]
 \subsubsection{Шаг 3. Проверка через $A_{fast}^{off}$}
 Выражение для $A_{fast}^{off}$ через константы модели (выводится из собственных векторов):
 \[
 A_{fast}^{off} = \frac{1 - \frac{k_3}{k_2}[B]}{1 + \frac{k_3}{k_4}[B]}.
 \]
 Подстановка найденных $k_2, k_3, k_4$ должна воспроизвести экспериментальную зависимость $A_{fast}^{off}([B])$. 
 \subsubsection{Шаг 4. Проверка через стационарную блокаду}
 Стационарная блокада при равновесии:
 \[
 \frac{I_B}{I_S} = \frac{[O^*]_{[B]\neq0}}{[O^*]_{[B]=0}} = \frac{1}{1 + \frac{k_1}{k_2}[B] + \frac{k_1 k_3}{k_2 k_4}[B]^2}.
 \]
 Сравнение рассчитанной кривой с экспериментальной служит финальной верификацией модели.
 \subsection{Численный пример (гипотетический)}
 Для иллюстрации: при $[B] = 10\ \mu\text{M}$ экспериментальные значения:
 \[
 \tau_{fast}^{off} = 1\ \text{с} \Rightarrow k_2 = 1\ \text{с}^{-1},
 \]
 \[
 \tau_{slow}^{off} = 10\ \text{с} \Rightarrow k_4 = 0.1\ \text{с}^{-1},
 \]
 \[
 1/\tau_{fast}^{on} = 1.1\ \text{с}^{-1} \text{ при } [B]=10\ \mu\text{M} \Rightarrow k_1 = 0.01\ \mu\text{M}^{-1}\text{с}^{-1}.
 \]
 Затем по формулам вычисляется $A_{fast}^{off}$ и $I_B/I_S$, сравнивается с экспериментом.
 \section{Заключение}
 В данном файле представлена общая методология вывода кинетической модели NMDA-канала. Для конкретной модели \textbf{<Название модели>} в соответствующих разделах следует подставить:
 \begin{itemize}
    \item конкретную схему переходов,
    \item матрицу $\mathbf{A}$ соответствующей размерности,
    \item аналитические выражения для $\tau_{fast}, \tau_{slow}, A_{fast}$,
    \item экспериментальные значения из статей (таблицы, графики).
 \end{itemize}
 \end{document}
--- a/НИР.docx
+++ b/НИР.docx
		`@ -0,0 +1 @@`
							`latexmk -pdf -outdir=pdf -auxdir=tmp templates/model_analitic.tex && latexmk -c -outdir=pdf -auxdir=tmp templates/model_analitic.tex`